Variability of annual and monthly rainfalls

[RWood]

From a fairly small set of locations' rainfall data I have looked at the variability of their rainfall. Statistically, a number called the coefficient of variation, which is the ratio of the standard deviation to the average, is a useful number to calculate. As an example, if a place averages 800mm annually and the standard deviation of the annual values is 160mm, then the CV is 160/800 = 0.2. Higher values indicate the most variability, lower values the least such, or greatest "reliability" in some sense. Here's some values for annual rainfall:

Napier, Christchurch, Tekapo, Mt Cook 0.22
Ashburton 0.21
Queenstown 0.20
Alexandra, Nelson 0.19
Dunedin 0.16
Milford Sd 0.15
Invercargill 0.13
Hokitika 0.12

The Mt Cook number seems a little surprising at first sight as one might expect the high-rainfall zones to have less variability. Its driest year (1930) had less than half of the annual average.

It's also instructive to look at the various monthly CV values. They more or less parallel the annual rankings, e.g:

Napier's range is from 0.57 to 0.94 (the latter is for March) and "average" 0.74
Mt Cook is again quite high with 0.48 to 0.70, average 0.60
Hokitika ranges from 0.35 (October) to 0.54, average 0.43.

The 2 extremes in the second list (0.94 and 0.35) do make sense - reliable spring rain on the West Coast, realtively erratic late summer/early autumn rainfall in Hawkes Bay.

[TonyT]

I'm not so sure just how useful the coefficient of variation is, given that the distributions of monthly and annual rainfall will be skewed, always out towards the high end. At the moment most people suggest a gamma distribution provides the best fit.

[RWood]

I'd still expect Mt Cook to show out as somewhat of an oddity though...its "spikes" are more pronounced than those of the other high-rainfall places I looked at.

[RWood]

OK then, here's another stat. which certainly tends to show up months or years with some very large monthly or annual excesses: looking at the skewness of the monthly and annual totals for the sites below. Of course, among the caveats is that the lengths of record vary from place to place, but they are all at least 65 years or so, over 100 in some cases. I don't have the tools to do any modelling analysis, just want to get a feel for the (un)evenness of the data.

Site Lowest & highest monthly skewness values Skewness of annual totals

Queenstown 0.63 (June) 2.36 (Aug) 0.82
Hokitika 0.05 (Nov) 1.26 (Mar) 0.13
Dunedin 0.54 (Nov) 2.53 (April) -0.13
Tekapo 0.72 (Oct) 3.27 (Nov) 0.15
Napier 0.77 (Aug) 2.04 (Mar) 0.49
Nelson 0.32 (June) 1.32 (Oct) 0.87
Invercargill 0.31 (Nov) 1.83 (Feb) 0.20
Mt Cook 0.61 (Jul) 1.74 (Dec) 0.21
Milford 0.36 (Jul) 1.47 (Feb) 0.25
Ch'ch Gdns 0.95 (Jan) 1.85 (April) 0.28

Dunedin has had a couple of extremely wet Aprils; its annual distribution looks unusual, being a bit loaded on the "wrong" side. Hokitika's Nov. values look almost symmetrical but are flatter than a normal distribution. Tekapo had an outstandingly high Nov. rainfall in 1967 (the month of the great late-season South Canterbury snow event). Nelson's monthly values show nothing startling but some of its annual values are very large, as is also the case for Queenstown.

[RWood]

Have got an interesting case with the site at Te Anau Downs - only 41 years' data, but thanks mainly to some extremely dry years in the middle and late 70s, its annual rainfall dist. is skewed quite strongly on the low side - though all of the monthly distributions show the "usual" pattern. Perhaps when the record is longer this anomaly will go away.

[tich]

Major individual rainfall events can have significant effects on monthly totals; sometimes occuring when rest of month's weather patterns are totally different. March 1988 would be probably regarded as being a month of cool dry west to southwesterly flows if it weren't for Cyclone Bola which delivered record rain to east of North Island.

[RWood]

Good point - a very big contrast between Bola and what followed, particularly for a large area of the country which had the dry SW flows followed by exceptionally high pressures and very dry sunny conditions in the April. Places like Nelson & Queenstown had virtually 6 weeks of clear dry weather.

[janewaystv]

Interesting that Invercargill's amongst one of the towns that ranks quite low when it comes to variability of rainfall, but of course there are some exceptions, Milford Sound - one place lower than IVC - surprising for me there as I thought MS had far more "reliable" rain than IVC.

Seems to me that eastern areas of NZ as well as the whole of the NI & N of the SI to a lesser extent experiences the largest variabilities of rainfall & western/ southern areas of the SI the least?

[RWood]

I think that's basically right, though as you can see form the "skew" figures all places have at least some months when there have been large deviations on the high side of the mean.